Apart from the quark and gluon kinetic and potential energies, the nucleon mass includes a novel energy of pure quantum origin resulting from anomalous breaking of scale symmetry. We demonstrate the effects of this quantum anomalous energy (QAE) in QED, as well as in a toy 1 + 1 dimensional non-linear sigma model where it contributes non-perturbatively, in a way resembling the Higgs mechanism for the masses of matter particles in electro-weak theory. The QAE contribution to the nucleon mass can be explained using a similar mechanism, in terms of a dynamical response of the gluonic scalar field through Higgs-like couplings between the nucleon and scalar resonances. In addition, the QAE sets the scale for other energies in the nucleon through a relativistic virial theorem, and contributes a negative pressure to confine the colored quarks.

除了夸克和胶子的动能和势能之外，核子质量还包括一种由尺度对称性异常破坏而产生的纯量子起源的新能量。我们展示了这种量子反常能量 (QAE) 在 QED 以及玩具 1 + 1 维非线性 sigma 模型中的影响，在该模型中它以类似于物质粒子质量的希格斯机制的方式无微扰地贡献在电弱理论中。QAE 对核子质量的贡献可以使用类似的机制来解释，即通过核子和标量共振之间的类似希格斯耦合的胶子标量场的动力学响应。此外，QAE 通过相对论维里定理为核子中的其他能量设定标度，并提供负压以限制有色夸克。